Asynchronous haptic simulation of contacting deformable objects with variable stiffness

International audienceAbstract--This paper presents a new asynchronous approach for haptic rendering of deformable objects. When stiff nonlinear deformations take place, they introduce important and rapid variations of the force sent to the user. This problem is similar to the stiff virtual wall for which a high refresh rate is required to obtain a stable haptic feedback. However, when dealing with several interacting deformable objects, it is usually impossible to simulate all objects at high rates. To address this problem we propose a quasi-static framework that allows for stable interactions of asynchronously computed deformable objects. In the proposed approach, a deformable object can be computed at high refresh rates, while the remaining deformable virtual objects remain computed at low refresh rates. Moreover, contacts and other constraints between the different objects of the virtual environment are accurately solved using a shared Linear Complementarity Problem (LCP). Finally, we demonstrate our method on two test cases: a snap-in example involving non-linear deformations and a virtual thread interacting with a deformable object

Model-Based Identification of Anatomical Boundary Conditions in Living Tissues

International audienceIn this paper, we present a novel method dealing with the identification of boundary conditions of a deformable organ, a particularly important step for the creation of patient-specific biomechani-cal models of the anatomy. As an input, the method requires a set of scans acquired in different body positions. Using constraint-based finite element simulation, the method registers the two data sets by solving an optimization problem minimizing the energy of the deformable body while satisfying the constraints located on the surface of the registered organ. Once the equilibrium of the simulation is attained (i.e. the organ registration is computed), the surface forces needed to satisfy the constraints provide a reliable estimation of location, direction and magnitude of boundary conditions applied to the object in the deformed position. The method is evaluated on two abdominal CT scans of a pig acquired in flank and supine positions. We demonstrate that while computing a physically admissible registration of the liver, the resulting constraint forces applied to the surface of the liver strongly correlate with the location of the anatomical boundary conditions (such as contacts with bones and other organs) that are visually identified in the CT images

Haptic Rendering Based on RBF Approximation from Dynamically Updated Data

In this paper, an extension of our previous research focused on haptic rendering based on interpolation from precomputed data is presented. The technique employs the radial-basis function (RBF) interpolation to achieve the accuracy of the force response approximation, however, it assumes that the data used by the interpolation method are generated on-the-fly during the haptic interaction. The issue caused by updating the RBF coefficients during the interaction is analyzed and a force-response smoothing strategy is proposed

Haptic Rendering of Interacting Dynamic Deformable Objects Simulated in Real-Time at Different Frequencies

International audienceThe dynamic response of deformable bodies varies significantly in dependence on mechanical properties of the objects: while the dynamics of a stiff and light object (e. g. wire or needle) involves high-frequency phenomena such as vibrations, much lower frequencies are sufficient for capturing dynamic response of an object composed of a soft tissue. Yet, when simulating mechanical interactions between soft and stiff deformable models, a single time-step is usually employed to compute the time integration of dynamics of both objects. However, this can be a serious issue when haptic rendering of complex scenes composed of various bodies is considered. In this paper, we present a novel method allowing for dynamic simulation of a scene composed of colliding objects modelled at different frequencies: typically, the dynamics of soft objects are calculated at frequency about 50 Hz, while the dynamics of stiff object is modeled at 1 kHz, being directly connected to the computation of haptic force feedback. The collision response is performed at both low and high frequencies employing data structures which describe the actual constraints and are shared between the high and low frequency loops. During the simulation, the realistic behaviour of the objects according to the mechanical principles (such as non-interpenetration and action-reaction principle) is guaranteed. Examples showing the scenes involving different bodies in interaction are given, demonstrating the benefits of the proposed method

Constraint-Based Simulation for Non-Rigid Real-Time Registration

International audienceIn this paper we propose a method to address the problem of non-rigid registration in real-time. We use Lagrange multipliers and soft sliding constraints to combine data acquired from dynamic image sequence and a biomechanical model of the structure of interest. The biomechanical model plays a role of regulariza-tion to improve the robustness and the flexibility of the registration. We apply our method to a pre-operative 3D CT scan of a porcine liver that is registered to a sequence of 2D dynamic MRI slices during the respiratory motion. The finite element simulation provides a full 3D representation (including heterogeneities such as vessels, tumor,. . .) of the anatomical structure in real-time

Biomechanical modelling of probe to tissue interaction during ultrasound scanning

Purpose: Biomechanical simulation of anatomical deformations caused by ultrasound probe pressure is of outstanding importance for several applications, from the testing of robotic acquisition systems to multi-modal image fusion and development of ultrasound training platforms. Different approaches can be exploited for modelling the probe-tissue interaction, each achieving different trade-offs among accuracy, computation time and stability. Methods: We assess the performances of different strategies based on the finite element method for modelling the interaction between the rigid probe and soft tissues. Probe\u2013tissue contact is modelled using (i) penalty forces, (ii) constraint forces, and (iii) by prescribing the displacement of the mesh surface nodes. These methods are tested in the challenging context of ultrasound scanning of the breast, an organ undergoing large nonlinear deformations during the procedure. Results: The obtained results are evaluated against those of a non-physically based method. While all methods achieve similar accuracy, performance in terms of stability and speed shows high variability, especially for those methods modelling the contacts explicitly. Overall, prescribing surface displacements is the approach with best performances, but it requires prior knowledge of the contact area and probe trajectory. Conclusions: In this work, we present different strategies for modelling probe\u2013tissue interaction, each able to achieve different compromises among accuracy, speed and stability. The choice of the preferred approach highly depends on the requirements of the specific clinical application. Since the presented methodologies can be applied to describe general tool\u2013tissue interactions, this work can be seen as a reference for researchers seeking the most appropriate strategy to model anatomical deformation induced by the interaction with medical tools

Intraoperative Biomechanical Registration of the Liver: Does the Heterogeneity of the Liver Matter?

International audienceBackground: Preoperative images such as computed tomography scans or magnetic resonance imaging contain lots of valuable information that are not easily available for surgeons during an operation. To help the clinicians better target the structures of interest during an intervention, many registration methods that align preoperative images onto the intraoperative view of the organs have been developed. For important organ deformation, biomechanically-based registration has proven to be a method of choice.Method: Using an existing biomechanically-based registration algorithm for laparoscopic liver surgery we investigate in this paper the influence of the heterogeneity of the liver on the registration result.Results: No statistical difference in the results was found between the registration performed with the homogeneous model and the one carried out with the heterogeneous model.Conclusion: As the use of an heterogeneous model does not improve significantly the registration result and increase the computation time we recommend to perform the type of registration task described in the paper with a simplified homogeneous model

Towards an Accurate Tracking of Liver Tumors for Augmented Reality in Robotic Assisted Surgery

International audienceThis article introduces a method for tracking the internal structures of the liver during robot-assisted procedures. Vascular network, tumors and cut planes, computed from pre-operative data, can be overlaid onto the laparoscopic view for image-guidance, even in the case of large motion or deformation of the organ. Compared to current methods, our method is able to precisely propagate surface motion to the internal structures. This is made possible by relying on a fast yet accurate biomechanical model of the liver combined with a robust visual tracking approach designed to properly constrain the model. Augmentation results are demonstrated on in-vivo sequences of a human liver during robotic surgery, while quantitative validation is performed on an ex-vivo porcine liver experimentation. Validation results show that our approach gives an accurate surface registration with an error of less than 6mm on the position of the tumor

Image-guided Simulation of Heterogeneous Tissue Deformation For Augmented Reality during Hepatic Surgery

International audienceThis paper presents a method for real-time augmentation of vas- cular network and tumors during minimally invasive liver surgery. Internal structures computed from pre-operative CT scans can be overlaid onto the laparoscopic view for surgery guidance. Com- pared to state-of-the-art methods, our method uses a real-time biomechanical model to compute a volumetric displacement field from partial three-dimensional liver surface motion. This permits to properly handle the motion of internal structures even in the case of anisotropic or heterogeneous tissues, as it is the case for the liver and many anatomical structures. Real-time augmentation results are presented on in vivo and ex vivo data and illustrate the benefits of such an approach for minimally invasive surgery